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Definition of "homotopy method" |
a technique for solving nonlinear algebraic equations F(x) = 0 based on higher-dimensional function embedding and curve tracing. The idea is to construct a parameterized function such that at one parameter value, say λ = λ0, the system of equations is easy to solve or has one or more known solutions, and at another parameter value, say λ = λf , the system of equations is identical to that of the system of interest, F(x) = 0. A homotopy method may then be interpreted as geometric curve following through solution space from the known solutions of the “easy” problem to the unknown solutions of F(x) = 0 |
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